Frobenius-Schur indicators of characters in blocks with cyclic defect

2019/01/18 by Murray, John
#20C20 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1901.06297

Abstract

Let p be an odd prime and let B be a p-block of a finite group which has cyclic defect groups. We show that all exceptional characters in B have the same Frobenius-Schur indicators. Moreover the common indicator can be computed, using the canonical character of B. We also investigate the Frobenius-Schur indicators of the non-exceptional characters in B. For a finite group which has cyclic Sylow p-subgroups, we show that the number of irreducible characters with Frobenius-Schur indicator -1 is greater than or equal to the number of conjugacy classes of weakly real p-elements in G.

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